Design equations for silicon detector ladders with heat generated by radiation damage induced leakage current

We find approximate analytical solutions to the problem of cooling a silicon detector ladder which is internally heated by leakage current caused by radiation damage. The heat generation term has an approximately exponential temperature dependence. heat is removed by convection and/or conduction to a heat sink. Design equations are derived which prevent thermal runaway, and a wide range of parameter space for those equations is explored.